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<pre>
      REAL             FUNCTION <a name="CLANHP.1"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>( NORM, UPLO, N, AP, WORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          NORM, UPLO
      INTEGER            N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      REAL               WORK( * )
      COMPLEX            AP( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CLANHP.19"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>  returns the value of the one norm,  or the Frobenius norm, or
</span><span class="comment">*</span><span class="comment">  the  infinity norm,  or the  element of  largest absolute value  of a
</span><span class="comment">*</span><span class="comment">  complex hermitian matrix A,  supplied in packed form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Description
</span><span class="comment">*</span><span class="comment">  ===========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CLANHP.26"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     <a name="CLANHP.28"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> = ( max(abs(A(i,j))), NORM = 'M' or 'm'
</span><span class="comment">*</span><span class="comment">              (
</span><span class="comment">*</span><span class="comment">              ( norm1(A),         NORM = '1', 'O' or 'o'
</span><span class="comment">*</span><span class="comment">              (
</span><span class="comment">*</span><span class="comment">              ( normI(A),         NORM = 'I' or 'i'
</span><span class="comment">*</span><span class="comment">              (
</span><span class="comment">*</span><span class="comment">              ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where  norm1  denotes the  one norm of a matrix (maximum column sum),
</span><span class="comment">*</span><span class="comment">  normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
</span><span class="comment">*</span><span class="comment">  normF  denotes the  Frobenius norm of a matrix (square root of sum of
</span><span class="comment">*</span><span class="comment">  squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NORM    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies the value to be returned in <a name="CLANHP.45"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> as described
</span><span class="comment">*</span><span class="comment">          above.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment">          hermitian matrix A is supplied.
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangular part of A is supplied
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangular part of A is supplied
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.  When N = 0, <a name="CLANHP.55"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> is
</span><span class="comment">*</span><span class="comment">          set to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP      (input) COMPLEX array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          The upper or lower triangle of the hermitian matrix A, packed
</span><span class="comment">*</span><span class="comment">          columnwise in a linear array.  The j-th column of A is stored
</span><span class="comment">*</span><span class="comment">          in the array AP as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">          Note that the  imaginary parts of the diagonal elements need
</span><span class="comment">*</span><span class="comment">          not be set and are assumed to be zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
</span><span class="comment">*</span><span class="comment">          where LWORK &gt;= N when NORM = 'I' or '1' or 'O'; otherwise,
</span><span class="comment">*</span><span class="comment">          WORK is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ONE, ZERO
      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, J, K
      REAL               ABSA, SCALE, SUM, VALUE
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.82"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.83"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CLASSQ.86"></a><a href="classq.f.html#CLASSQ.1">CLASSQ</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, REAL, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 ) THEN
         VALUE = ZERO
      ELSE IF( <a name="LSAME.95"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'M'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find max(abs(A(i,j))).
</span><span class="comment">*</span><span class="comment">
</span>         VALUE = ZERO
         IF( <a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
            K = 0
            DO 20 J = 1, N
               DO 10 I = K + 1, K + J - 1
                  VALUE = MAX( VALUE, ABS( AP( I ) ) )
   10          CONTINUE
               K = K + J
               VALUE = MAX( VALUE, ABS( REAL( AP( K ) ) ) )
   20       CONTINUE
         ELSE
            K = 1
            DO 40 J = 1, N
               VALUE = MAX( VALUE, ABS( REAL( AP( K ) ) ) )
               DO 30 I = K + 1, K + N - J
                  VALUE = MAX( VALUE, ABS( AP( I ) ) )
   30          CONTINUE
               K = K + N - J + 1
   40       CONTINUE
         END IF
      ELSE IF( ( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) .OR. ( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'O'</span> ) ) .OR.
     $         ( NORM.EQ.<span class="string">'1'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find normI(A) ( = norm1(A), since A is hermitian).
</span><span class="comment">*</span><span class="comment">
</span>         VALUE = ZERO
         K = 1
         IF( <a name="LSAME.126"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
            DO 60 J = 1, N
               SUM = ZERO
               DO 50 I = 1, J - 1
                  ABSA = ABS( AP( K ) )
                  SUM = SUM + ABSA
                  WORK( I ) = WORK( I ) + ABSA
                  K = K + 1
   50          CONTINUE
               WORK( J ) = SUM + ABS( REAL( AP( K ) ) )
               K = K + 1
   60       CONTINUE
            DO 70 I = 1, N
               VALUE = MAX( VALUE, WORK( I ) )
   70       CONTINUE
         ELSE
            DO 80 I = 1, N
               WORK( I ) = ZERO
   80       CONTINUE
            DO 100 J = 1, N
               SUM = WORK( J ) + ABS( REAL( AP( K ) ) )
               K = K + 1
               DO 90 I = J + 1, N
                  ABSA = ABS( AP( K ) )
                  SUM = SUM + ABSA
                  WORK( I ) = WORK( I ) + ABSA
                  K = K + 1
   90          CONTINUE
               VALUE = MAX( VALUE, SUM )
  100       CONTINUE
         END IF
      ELSE IF( ( <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'F'</span> ) ) .OR. ( <a name="LSAME.157"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'E'</span> ) ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Find normF(A).
</span><span class="comment">*</span><span class="comment">
</span>         SCALE = ZERO
         SUM = ONE
         K = 2
         IF( <a name="LSAME.164"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
            DO 110 J = 2, N
               CALL <a name="CLASSQ.166"></a><a href="classq.f.html#CLASSQ.1">CLASSQ</a>( J-1, AP( K ), 1, SCALE, SUM )
               K = K + J
  110       CONTINUE
         ELSE
            DO 120 J = 1, N - 1
               CALL <a name="CLASSQ.171"></a><a href="classq.f.html#CLASSQ.1">CLASSQ</a>( N-J, AP( K ), 1, SCALE, SUM )
               K = K + N - J + 1
  120       CONTINUE
         END IF
         SUM = 2*SUM
         K = 1
         DO 130 I = 1, N
            IF( REAL( AP( K ) ).NE.ZERO ) THEN
               ABSA = ABS( REAL( AP( K ) ) )
               IF( SCALE.LT.ABSA ) THEN
                  SUM = ONE + SUM*( SCALE / ABSA )**2
                  SCALE = ABSA
               ELSE
                  SUM = SUM + ( ABSA / SCALE )**2
               END IF
            END IF
            IF( <a name="LSAME.187"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
               K = K + I + 1
            ELSE
               K = K + N - I + 1
            END IF
  130    CONTINUE
         VALUE = SCALE*SQRT( SUM )
      END IF
<span class="comment">*</span><span class="comment">
</span>      <a name="CLANHP.196"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a> = VALUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="CLANHP.199"></a><a href="clanhp.f.html#CLANHP.1">CLANHP</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

</pre>

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